product rule
Differentiating combined functions
The product rule is a formula in calculus for finding the derivative of two functions multiplied together.
If you have f(x) times g(x), the derivative equals f times the derivative of g, plus g times the derivative of f.
Students often memorize it as (fg)' = f'g + fg'.
The rule extends to products of more than two functions.
Recognizing meaningful differences
- derivativeFunction's rate of change
- tangent lineCurve-touching straight path
- slopeAngled terrain or steepness
- rate of changeMeasure of variation speed
function · variable · polynomial · exponent · trigonometric functions · critical point · inflection point · optimization
Product-finding operation
- factorContributor to result
- multiplicandNumber being multiplied
- multiplierNumber that scales another
- timesOccurrences or multiplications
integer · decimal · commutative property · associative property · distributive property · calculation · equation · algorithm
Quantity multiplying proportionally over time
- compound interestReturns on reinvested earnings
- doubling timeTime to grow twofold
- rate of changeMeasure of variation speed
- accumulationCollected mass over time
logarithmic scale · decay rate · continuous growth · differential equations · modeling · projection · proliferation
Point where paths meet
- outcomeFinal result of events
- likelihoodChance something will occur
- combinatoricsMathematics of discrete enumeration
- stochasticRandomly determined, statistically describable
differentiation
Recognizing meaningful differences
- derivativeFunction's rate of change
- tangent lineCurve-touching straight path
- slopeAngled terrain or steepness
rate of change · function · variable · polynomial · exponent · trigonometric functions · critical point · inflection point · optimization · integral
multiplication
Product-finding operation
- factorContributor to result
- multiplicandNumber being multiplied
- multiplierNumber that scales another
times · integer · decimal · commutative property · associative property · distributive property · calculation · equation · algorithm · mental math
exponential growth
Quantity multiplying proportionally over time
- compound interestReturns on reinvested earnings
- doubling timeTime to grow twofold
- rate of changeMeasure of variation speed
accumulation · logarithmic scale · decay rate · continuous growth · differential equations · modeling · projection · proliferation
intersection
Point where paths meet
- outcomeFinal result of events
- likelihoodChance something will occur
- combinatoricsMathematics of discrete enumeration
stochastic · random variable · expected value · probability distribution
- Formulaschemical formula, quadratic formula, empirical formula, area formula, volume formula
- Math RulesPythagorean theorem, distributive property, commutative property, associative property, order of operations
- calculusderivatives, integral, integrals, limits, differential calculus
- combinatoricspermutation, combinations, combination, counting, arrangements
- Logarithmslogarithm, log, ln, natural log, natural logarithm
- limit methodsTaylor expansion
rule, produce, product, production, products, producer, produced, productive, producing